Oh dearie me, oh my. This is just a horrible mistake by Jeremy Grantham here. I agree that he's a vastly better investor than I am, no doubt hugely more intelligent as well. But this really is a basic, schoolboy error.

Then there is the impending shortage of two fertilizers: phosphorus (phosphate) and potassium (potash). These two elements cannot be made, cannot be substituted, are necessary to grow all life forms, and are mined and depleted. It’s a scary set of statements. Former Soviet states and Canada have more than 70% of the potash. Morocco has 85% of all high-grade phosphates. It is the most important quasi-monopoly in economic history.

What happens when these fertilizers run out is a question I can’t get satisfactorily answered and, believe me, I have tried. There seems to be only one conclusion: their use must be drastically reduced in the next 20–40 years or we will begin to starve.

And I'm afraid that it really is a schoolboy mistake. He's drawing his numbers from "reserves" without understanding what reserves means. It absolutely does not, at all, mean all of whatever it is out there. It is, rather, an economic construct.

Just to check here are the US Geological Survey (the usual source for this sort of information) reports for phosphate rock and potassium. Yes, you can see where he's getting his numbers from, the Moroccan (actually, plus Western Sahara) guys do have 50 somethings of the 71 somethings of reserves. Yes, ex-Soviets and Canada have most of the potash reserves.

But reserves aren't the important number. As I explained elsewhere at length and as I wrote it I can quote it at length:

To a useful level of accuracy the mining world divides the world up into dirt and ore. Your allotment patch contains gold, rare earths, uranium and all sorts of other lovely metals. However, your allotment patch is dirt. For while we do know how to extract all of those metals the cost of doing so would be higher than any value that could be recovered.

Ore is simply dirt where we know how to extract the metals: and also the value of the metals is higher than the cost of extraction. Ore is an economic concept, not a natural world one. And as with so many other economic concepts what is dirt and what is ore is a constantly changing spectrum. For technology, including the technology of extraction, changes over time. As an example I'm about to embark on the extraction of tungsten from some left over rock. A century ago, when it was dug up, it was rock. Now it's ore. The extraction technology has changed over time.

We should also go one stage even further and talk about Donald Rumsfeld's known unknowns.

When you see an environmentalist complaining that we're going to run out of a mineral in a generation he'll actually be correct. That's also the number Madsen uses for copper, 40-60 years or so. For every generation runs out of mineral reserves, this has been true since we started mining. For what everyone is talking about is "reserves". These are the known knowns. These are the ore, we know where it is, we know we can extract it at current prices, with current techniques, and make a profit doing so. Further, we have also tested and proven all of this to the satisfaction of the stock market listing rules where mining companies go to get traded.

You'll not be surprised to learn that drilling and sampling and sending odd hairy geologists over the hill with little hammers is expensive. So we only do this with the stuff we're likely to dig up in the next few decades. Thus, reserves of ore are, at any one time, good for only a few decades of use. Because they are a both legal and economic concept and as such we only define as reserves what we're likely to use in the next few decades. Or rather, only bother to do enough work to declare as reserves what we're likely to use in the next few decades. Thus every generation does indeed use up the available reserves of minerals.

But that isn't all there is of course: there's also the known unknowns. We've only bothered to stake out this side of the hill and in a couple of decades we'll do the same to the other side. We know it's there, we've just not bothered to prove it yet. These are more generally known as resources. They're there, we know that, we've just not gone through the expense of converting them to reserves yet.

Then there's our unknown knowns. We do know roughly what the geology of many places is. But we've sent very few hairy odd men with hammers over it. For example, we know that the geology of Madagascar is quite similar to that of the German/Czech border. Lots of lovely tungsten, tantalum, niobium, scandium up in them thar hills. Same sort of volcanic structure that's been folded in a similar manner and weathered much the same way. But why bother with the lemurs when you can go digging within reach of the Pilsener Urquel brewery? Well, quite. We're sure there's lots out there. Not sure quite where, in what quantities, quite how we'd get it out: an unknown known.

And then there's the unknown unknowns. The best way to approach this is from the other side. We think we know what the crustal abundance of all (OK, most) metals is. At the extreme we can imagine mining your allotment for them. Whether or when we'll get the technology to do so at economic cost we don't know. We do know that we can do it right now but only at exorbitant cost. Take, say, Tellurium, that we use to make a certain type of solar cell. Crustal abundance is, well, I can't remember how many zeroes there are after the decimal point to be honest. 0.1 parts per million? 0.0001 ppm? Somewhere in that range meaning that in the crust of the earth there's some 120 million tonnes of the stuff (I do recall that number from having done the calculation).

We use 125 tonnes of tellurium globally each year. Our known known is that we get it from copper slimes (no, real mining word, one of the wastes of making copper). We make enough to cover current demand from our known known. We're pretty sure about the known unknown as well: there's mountains just full of copper out there which contain that Te. Our unknown known is that there are other minerals that contain it in some quantity but we've just never bothered to check. And our unknown unknown is that, if it ever became expensive enough, I'd be around rootling through your veg patch to get it.

Reserves, the numbers that Grantham is using, are the deposits that we know where they are, have drilled and tested them, we know how to extract and process them using current technology and we also know that we can make a profit doing so. They are the known known: and yes, this really is the number that Grantham is using.

Resources is a very different number. This is a combination of the unknown knowns and the known unknowns described above. For potash?

Estimated world resources total about 250 billion tons.

At the current usage rate of 33 million tonnes a year that gives us an over 7,000 year supply. For phosphate rock?

World resources of phosphate rock are more than 300 billion tons.

At the 190 million tonne a year usage, a 1,500 years supply.

And this is before we get onto the unknown unknowns, the actual amount of the two elements that the planet itself contains. Considerable amounts in fact. Phosphorus being some 0.1% of the lithosphere (ie, the top part of the Earth). Potassium perhaps 2.5%. Given that the lithosphere weighs something like 300 billion, billion, tonnes, I have a very strong feeling that that's enough for us to be going on with.

I'm afraid that Grantham is just horribly, horribly, wrong here. He is looking at mine reserves as if they're the total amount of the elements available to us. Which mine reserves are not. Mine reserves are a mixed economic/legal concept, the amount of specific ore that we've bothered to properly map out, measure, test and prove that we can extract and make a profit on using current technologies and current prices.

Resources is the more accurate figure to use for societal availability over any reasonable time period. And by the time we start talking about a thousand or two years in the future then total elemental abundance is the correct number.

Grantham may indeed know how to make money. But I really would suggest a technical dictionary the next time he wants to talk about mine reserves and the availability of resources. For this is just an awful, schoolboy type, error of his.